
p 










NOTES ON 


MECHANICAL DRAWING 


J. D. PHILLIPS 
H. D. ORTH 



UNIVERSITY OF WISCONSIN 
MADISON 
1911 



COPYRIGHT, 1911 

BY 

J. D. PHILLIPS 
H. D. ORTH 


TRACY, GIBBS & CO. 
PRINTERS 

7 



©Cl. A 2 9212 9 








CHAPTER 1 


DRAWING INSTRUMENTS AND MATERIALS 

THEIR SELECTION - MANIPULATION AND CARE 


1. General. The thing of prime importance to the student 
in beginning Drawing is a good set of instruments. He had 
better have a fewer number and those of standard quality, than 
a variety of poorly constructed, cheap instruments. Beginners 
often think that a cheap set will do to learn with and a good set 
can be secured afterward. But it must be emphasized that 
while the student is learning is the time when he forms his draft¬ 
ing habits and sets his standard of excellence. He is inexperi¬ 
enced in handling the drafting instruments and hence, to obtain 
the best results, the best instruments are none too good. With 
a good set of instruments he is able to reach a degree of excel¬ 
lence consistent with his ability; he has a fair chance to make 
good, while with a poor set he is handicapped from the start, 
and can never obtain the results he might have obtained with a 
better set. It is difficult to define a “good” set of instruments 
so that the beginner will recognize them, for the better grades 
are extensively imitated, and he should be guided in his selec¬ 
tion either by some more experienced draftsman, or the trade 
mark and the price set by some reliable dealer. 

A good set differs from a poor one mainly in, that they are 
made of better material, are tempered correctly so that when 
once sharpened will remain so for a reasonable length of time, 
and the workmanship is such that they retain their alignment 
and adjustment when handled with reasonable care. These 
things can only be known definitely after the set has been given 
a fair trial. 


Next to a good set of instruments is this consideration: they 
must be taken care of ,—for as with any other delicate mechan¬ 
ism, the best results can only be reached when care is taken in 
their adjustment and the working parts kept in prime condition. 
It is often difficult to impress upon the student the importance 
of having a ruling pen or needle point sharp, or a compass joint 
nicely adjusted, but after some experience he will surely agree 
that perfection can never be attained with imperfect or poorly 
adjusted instruments. 

2. Drawing 1 Boards. The drawing board should be made of 
well seasoned, straight grained, soft wood; free from knots and 
cracks. The best boards are designed to prevent warping, vari¬ 
ous means being used to accomplish this end. Some are built 
up of small strips glued together; others have a series of saw 
cuts in the back running lengthwise of the grain to reduce the 
transverse strength and are made rigid by cleats of hard wood 
screwed through slots equal in width to the diameter of the 
screw. This arrangement allows the board to expand and con¬ 
tract, the screws sliding back and forth in the slots. 

(a) Tests. To test the surface of the board place a standard 
straight edge upon it in various positions and with the board 
held up to the light notice whether the straight edge is in con¬ 
tact with the surface at all points. Test the working edge of 
the board similarly. 

( b) Care. The surface and edges of the drawing board 
should be kept free from cuts, scratches, and bruises. Paper 


[ 3 ] 



should be cut on the bach of the board. The board should not be 
subjected to extremes of temperature and moisture. 

3. The T-Square is used for drawing parallel horizontal 
lines, and for directing the motion of the triangles. It consists 
of a rule called the blade attached to one end of which is a 
cross-piece called the head, which directs the motion of the blade 
by being pressed against the edge of the board. Lines are 
always ruled along its upper edge. The head is sometimes made 
movable so as to draw parallel lines in any direction. The blades 
are made of various kinds of wood, and of steel, or rubber. 
The most common forms are made of wood with edges of 
ebony, or celluloid. The steel blade is the most accurate, but 
tends to soil the drawing and smear dry ink lines. 

The requirements are that the under surface of the blade shall 
be plane, and the working edge of the head and blade straight. 
It is not necessary that the edge of the blade be at right angles 
to the head. 

(а) Tests. The best method for testing the edges of a 
T-square is a comparison with a standard straight edge. The 
edges of the blade may be otherwise tested as follows: Draw a 
line along the edge of the blade through two points on the paper, 
and mark the position of the end of the blade. Now swing the 
square around to reverse the ends of the blade with respect to 
the ruled line, keeping the same side up and bringing the same 
edge to the ruled line, with the end on the mark and rule a 
second line through the two points. If the two lines coincide 
the blade is straight. In using the square the head should be 
held firmly against the edge of the board with the left hand, the 
ruling being done with the right. 

(б) Care. Great care should be taken to preserve the square 
from injury. The upper edge should always boused for ruling, 
and should be kept free from cuts and bruises. It should never 
be used as a guide for the knife in cutting paper. If a straight 
edge is necessary in trimming drawings use the lower edge. 

4. Triangles are used for drawing perpendiculars and lines 
at various angles, and for ruling parallel lines. . They are made 


of wood, rubber or amber. The rubber and amber are the more 
accurate and the amber has the double advantage over the rub¬ 
ber that it does not attract dirt and soil the drawing, while it 
permits the lines to be seen through it. The forms most com¬ 
monly used are the 45° and 60° triangles. With these any 
multiple of 15° can be constructed. Other forms are used for 
special purposes. 



(a) Tests. The edges of a triangle should be straight and its 
angles true. The edges are best tested with a straight edge,'— 
otherwise by reversion as explained for the T-square. The right 
angle may be tested as follows; Place the triangle in position 
D as shown in Fig. 1, and draw the line AB. If when the tri¬ 
angle is turned over into position C, the edge coincides with the 
line AB the angle is 90°. 

When the right angles have been found true, the 45° angles 
are true if equal, and the 30° and 60° are true if one is double 
the other. These points may be tested by constructing the 
angles on paper thus: For the 45° angle draw a 45° line with 
one of the angles and bringing the other into the same position 
see if the edge coincides with the line. For the 30°, 60° tri¬ 
angle place the short leg against the T-square and draw two 60° 





























lines through a point by reversing the triangle so that the lines 
make angles on opposite sides of the vertical. (See Fig. 1.) 
Now draw a horizontal line cutting the two lines. If the triangle 
formed is equilateral, which may be ascertained with the divid¬ 
ers, the 60° angle, and also the 30°, is true. 

(&) Triangle and T-square Combinations. To draw lines 
making 15°, 30°, 45°, 60°, and 75° with the horizontal. (See 
Figs. 2 and 3.) 


\! 

0 

•i i 1 

—?— 

/ 

/y—sc° 

o 

< 







o 




Q 

n 







Fi&. 2 . 



The pencil should always be drawn away from the T-square. 
In drawing a line through a given point in a line the T-square 
should be moved away from the line so that the edge of the tri¬ 
angle passes through the point. This principle holds in any 
combination. The straight edge which guides the motion of the 
ruling edge should not pass through the point through which 
the line is to be drawn. 



(c) Triangle Combinations. Lines parallel or perpendic¬ 
ular to an obligue line , or making with it angles of 15°, 30°, 45°, 
60°, and 75°. 

For example, to draw a line parallel to AB through C. (Fig. 
4, A.) Place triangle D so that one edge coincides with AB 


Fig.3. 


[ 5 ] 

































































and fit triangle E against it. With E held firmly in place by 
the left hand, slide D along until the edge passes through C. 

In Fig. 4 the black triangle represents the fixed triangle and 
the dotted one is the movable one set upon the line. The full 
line shows the position in which the movable triangle guides the 
pencil, or the position of the triangle substituted for it. 

5. Scales are used for making measurements and laying off 
distances. They are made of paper, ivory, boxwood, rubber, 
and steel, and are divided into all convenient units. The usual 
forms are the flat with beveled edges, and the triangular. 

The scale should be perfectly straight, the edges should be 
thin, sharp and free from nicks, and the graduations very fine 
clear-cut lines. The scale is usually a little over 12" long, and 
is graduated for a distance of 12". 


X 

-- 2 

- 

Iy 




1 

18 

20 

ri|T 

If 1 

T 

IT 

ijri 

i 

l 

S * 

’ 1 

o : 

3 

6 9 




Fig: 5. 


(a) The architect's scale is divided on one face into inches, 
halves, quarters, eights and sixteenths of an inch. The other 
five faces of the triangular scale have two scales each, one being 
one-half the other. To illustrate the reading of these scales, 
consider the one designated by a figure 1 at the end, which indi¬ 
cates that the scale reads 1 foot for each inch of the scale. The 
inch to the right of the 0 at the right end is divided into 48 
equal parts so that each of the smaller divisions represents i", 
and the spaces marked 3, 6, 9 represent 3" each. To the left 
of the 0 the readings 1, 2, etc., are inches, and of course 
represent feet. Now to measure off for example a distance of 
2 ft. 4^ ins. to the right of a point (Fig. 5), place the 2 opposite 
the point X and read to the right past the 0, 4| ins. to the point 
Y. In case you wish to read to the left place the 4-j in. mark to 
the point and read to the left through 0 to the 2. 

The scale should never he used as a straight edge in ruling 
lines. 


6. Pencils. The lead of the drawing pencils should be of 
fine, even grain and of a hardness suited to the paper upon which 
the drawing is to be made. It should give a fine, firm, clean-cut 
line without pressure enough applied to crease the paper, so that 
in case it is necessary to erase no marks are left to disfigure the 
drawing. These properties may best be determined by trial. 
For the Duplex paper a 4H to 6H will be found suitable for the 
mechanical line work, and for the freehand work—letters and 
figures, a 2H to 4H is satisfactory. 

7. Sharpening’ the Pencil and Compass Leads. The pencil 
point is one of the things most neglected by beginners and yet 
it is one of the most important of all the drawing instruments, 
requiring more frequent and patient attention to secure good 
results. A dull or improperly sharpened pencil is not only in¬ 
accurate, but produces a mussy drawing, a thing which is almost 
certain to give an unfavorable impression of the student’s ability 
as a draftsman. 



FIg. 6. 


(а) The Ruling Point. For ruling lines the wood should be 
cut away until about f" to of lead is exposed and this should 
then be ground to a chisel shaped point by rubbing opposite 
sides on a fine file or sand paper pad, holding the pencil at an 
angle of a few degrees to the plane of the pointer. Having pro¬ 
duced a thin edge, round the corners slightly by rotating the 
pencil about its axis slowly while the former grinding motion is 

continued. (See Fig. 6.) Compass leads should be sharpened 
in the same manner. The chisel point is particularly effective 
where a large number of long lines must be drawn. 

(б) The Measuring Point. For laying off distances the point 
should be conical and very sharp. It is a good plan to sharpen 
one end of the pencil for ruling and the other for measuring. 
For freehand work the point should be conical but somewhat 
more blunt than the measuring point. 
































(c) Manipulation. The pencil should always be pressed very 
lightly upon the paper. In ruling along a straight edge care 
must be taken to hold the pencil constantly at the same inclina¬ 
tion to the paper; i. e., move it parallel to itself. This is 
necessary in order that the line drawn be straight and parallel to 
the ruling edge. The rule should be flat upon the paper. Points 
should not be obliterated with pencil lines. If several lines are 
to be drawn through a point it is better to stop them a short 
distance from the point, so as to leave it clearly defined. A 
small circle should be drawn around points to indicate their 
position instead of making the points heavy. 

8. Compasses are used for drawing circles or arcs of circles. 
For very large circles the lengthening bar may be added, and 
when this does not suffice, a beam compass may be used. The 
bow compass is best for circles under f" radius. 

(a) Construction . They are best made of rolled German sil¬ 
ver, and should combine lightness with rigidity. The vital part 
of the compass is the head which in the modern instruments 
consists of two discs forming the heads of the legs held in appo¬ 
sition in a fork by means of two pivot screws, which also serve 
to adjust the bearing. The top of the fork terminates in a 
handle. The thing next in importance is the socket joint of the 
removable pen and pencil parts. 

(&) Tests. All joints in a compass and its parts should work 
in the same plane. To test the compass for this, place the parts 
in the socket and bend the legs out at the head, and then bring 
the points together by bending at the lower joints. If the points 
come exactly together the joints are true. This is also a test of 
the alignment of the shank in the socket. 

( c) Setting the Lead. Before attempting to use the compass 
the lead should be sharped as described under “Pencils” and set 
as follows: Place the pen in the compass and adjust the needle 
so that it projects slightly beyond the nibs of the pen; remove 
the pen, replace the pencil and adjust the lead so that it is 
slightly shorter than the needle point. 

(d) Manipulation. In describing a circle the needle point 


and pen or pencil parts should be bent so that they are perpen¬ 
dicular to the paper. The needle point will then make only a 
small hole, and the nibs of the pen will bear equally upon the 
paper, which is a condition that must be fulfilled in order that 
the line may not be ragged. 

Having set the compass approximately and adjusted it exactly 
with the hair-spring thumb-screw, grasp the handle between the 
thumb and forefinger and, with the needle point resting lightly 
on the center, and the compass leaning a little in the direction 
of motion, start with the lead or pen about under the wrist and 
swing in the circle without stopping. The motion should be 
in a clockwise direction. Let one passing of the lead or pen 
suffice. Do not go over the line again either backward or for¬ 
ward. 

When using the lengthening bar, the length of which makes 
the instrument somewhat unwieldy, the pen or pencil part should 
be steadied by grasping it lightly between the thumb and fore¬ 
finger of the free hand. 

(e) Care. The compass should be carefully guarded against 
injury. Falling on the floor may spoil the alignment. The 
needle point should always be very sharp. When dull it may 
either be sharpened on a fine grained oil stone or replaced by a 
new one. It is a common fault with beginners to clamp the 
points and head joint too tight, with the idea that they will 
remain more securely in place. The joint should work easily. 
If clamped too tight it is difficult to set the points to the required 
distance as they will spring slightly when released. The screws 
should not be set down hard in clamping the points as this 
destroys the screw threads. The points will remain securely in 
place with careful handling if clamped lightly. 

9. Dividers are very similar to compasses in general appear¬ 
ance, the difference being that they usually have no lower joints, 
and that they have two very sharp points of steel. When closed 
they have the appearance of a single conical point. They are 
used either for laying off distances from the scale, or for trans¬ 
form g lengths from one part of a drawing to another. They 


may also be used to divide a line either straight or curved into 
any number of equal parts. 

(a) Manipulation. A line is divided into a small number of 
equal parts by trial. First the required fractional length is 
estimated and then stepped off on the line. If it is not correct 
the first time an adjustment is made according to the size of the 
error. In stepping off distances on a line the dividers should be 
held by the handle between the thumb and forefinger, and swung 
alternately on one side of the line and the other. The plane of 
the legs should be perpendicular to the paper 

Do not make large holes in the paper. 

10. Bow Pen, Bow Pencil and Bow Dividers. The bow 

pen and pencil serve the same purposes as the compass, and the 
bow dividers take the place of the large dividers, in describing 
small circles, and laying off small distances, where the larger 
ones are too heavy and less accurate. They have the advantage 
that they retain their adjustment. 

11. Ruling 1 Pen. This is most used of all the instruments 
and should therefore claim considerable attention in its selection, 
manipulation and care. It is used for ruling lines in ink. 

(a) Construction. It consists of two blades of steel connected 
by a screw for regulating the distance between the points, and 
these surmounted by a handle of wood, ivory, bone, or alumi¬ 
num. One of the blades is usually provided with a joint or 
other device by means of which the blades may be spread apart 
for cleaning. The qualities that a ruling pen should possess are 
as follows: The steel should be of such quality as to retain 
a smooth sharp edge; the blades should be of the same length, 
and the inner one sufficiently stiff to resist a light pressure 
against the ruler; the points should be of the same width equally 
rounded and directly opposite each other. 

(&) Manipulation. In using the pen it should be held in a plane 
perpendicular to the surface of the paper, the handle inclined a lit¬ 
tle to the right and the blades in a plane parallel to the ruling edge. 
It is held between the thumb and first and second fingers, the 
knuckles bent so that it may be held at right angles to the 


length of the hand, and with the points of the pen pressing 
lightly upon the paper. With the pen in this position draw it 
rather slowly from left to right. The motion should be one of 
the shoulder and elbow without bending the wrist. Keep the 
forearm always perpendicular to the line being drawn , at tvhai- 
ever angle to the horizontal. Endeavor to get into the easiest 
position for inking a line, even though it becomes necessary to 
walk around the drawing. The best results are secured by 
standing while inking. Care should be taken that the points of 
the nibs do not approach the ruling edge too closely or the ink will 
be drawn under by capillary attraction. When the line is inked 
move the ruling edge away from it to avoid blotting. Do not 
press the side of the pen point too heavily against the ruling 
edge, as the nibs will be pushed together and the width of 
line will vary. A certain touch, familiar to good draftsmen, 
brings the pen lightly but firmly in contact with both the cloth 
and the ruling edge. Steady the hand by sliding it on the end 
of the little finger. The pen should be moved from left to right, 
and should be drawn, not pushed. 

(c) Blotting. With care blotting may always be avoided. It 
may be caused by (1) ink flowing under the rule by capillary 
attraction, (2) moist ink on the outer surface of the blade in 
contact with the ruler drawing ink by capillary attraction from 
between the nibs and finally to the paper, (3) touching the 
edge of the rule with the point of the pen in lifting it from the 
paper, (4) by drawing a line over a moist portion of the paper 
or over one that has been roughened by erasing, (5) filling the 
pen too full so that the ink is not sustained by capillary attrac¬ 
tion. 

(d) Filling the Pen. The pen is filled by drawing the quill 
attached to the stopper of the ink bottle between the nibs. 
When filled the ink should not stand more than to f" from 
the end of the nibs to avoid blotting. When the ink does not 
flow freely from the pen it should be removed, the pen thor¬ 
oughly cleaned and supplied with fresh ink. 

(e) Care. Clean the pen while in use by inserting a piece of 


cloth between the blades and drawing it out through the nibs 
without moving the thumbscrew. Ink dries quickly so that the 
pen should not be laid aside for any length of time without 
cleaning. After using the pen it should be carefully cleaned by 
separating the nibs and wiping with a piece of chamois skin or 
one of the pen wipers which come with prepared inks. If the 
ink is allowed to corrode it may ruin the surface of the nibs, 
thereby spoiling the pen. 

(/) Setting and Grinding the Pen. The blades should be of 
precisely the same length, the points of the same width, rounded 
in two directions, and as sharp as they can be made without 
producing the sensation of cutting. They should not scratch 
the paper when drawing a line. This occurs if they are sharp¬ 
ened to a point instead of a rounded edge, or if the point is 
rough or notched. Any irregularities in the length of the points 
may be detected by holding the pen up to the light so as to see 
both points, and then closing them slowly. 

In case of irregularities or the pen becoming dull from use it 
may be treated as follows: Close the nibs until they just touch 
each other and then, using a close-grained oil stone, hold the 
pen as though to draw a line and draw it back and forth, revolv¬ 
ing it slowly in the plane of motion which is perpendicular to 
the plane of the stone. This will dull the nibs, but it will grind 
them into the desired rounded point. Grind until the nibs are 
of equal length. If the pen now be held up to the light with 
the nibs separated and the points directed to the eye so as to 
catch the angle of reflection of the light, a bright speck will be 
seen on the points. This must be reduced by rubbing the out¬ 
side of the nibs on the oil stone, giving at the same time a slight 
rotary motion to the handle, which is held at an angle of 15° or 
20° with the face of the stone; the point of the pen being exam¬ 
ined from time to time, and the process continued until the 
point is as fine as can be used without cutting the paper. 

All grinding should he done on the outside of the nibs. To 
remove the burr from the inside use a piece of leather or soft 
pine. 


Considerable care and patience are necessary to put the pen 
in good working condition, but every draftsman should learn to 
grind his own pens, sharpen needle points, etc., thereby saving 
considerable time and trouble. 

12. Paper. The requisites of a drawing paper depend upon 
the character of the drawing to be made, and we need only con¬ 
sider the qualities essential to a paper suitable for ordinary shop 
drawings. 

The paper should be strong, must stand erasure without spoil¬ 
ing the surface. As the drawings are to be traced the inking 
qualities need not be considered. Whatman’s hot pressed is 
very satisfactory for precise line drawings. It has a smooth 
surface and stands erasure very well, but on account of being 
expensive is not much used in commercial drafting offices. 
Detail paper comes in rolls and is much cheaper and of inferior 
quality, but quite extensively used in office practice where work¬ 
ing drawings are to be made and traced. It is of buff color, 
has a smooth surface and does not stand erasing very well. An 
excellent paper for fine pencil drawings is the Duplex. There 
are many other styles and makes of paper on the market each 
having its particular advantages and disadvantages, for a de¬ 
scription of which see dealers’ catalogue. 

13. Tracing’ Cloth is the medium most generally used for 
reproducing the original drawing in the form of prints. It is a 
firm transparent cloth covered with a sizing. The side on which 
the sizing is placed is very smooth and glassy, while the other 
side is less so. 

The time worn question of which side of the cloth is to be 
used is best decided by considering the nature of the work to be 
done. The glazed side was primarily intended for use and 
hence was rolled in, but the cloth will curl when inked on this 
side. From the fact that there is more sizing on the glazed 
side, the ink, especially red ink, does not eat so deeply into the 
cloth and hence is more easily erased from this side. If work is 
to be done in pencil it must be done on the dull side in order 
that the pencil lines show. The dull side takes ink more readily, 


without so much danger of blotting, and the cloth does not curl. 
In general it is safe to say that where much erasing is to be done 
the bright side is preferable, but where penciling is to be done 
on the cloth the dull side must be used. Beyond these con¬ 
siderations the choice rests entirely with the draftsman. 

If the surface of the cloth appears greasy so that it does not 
take the ink readily, it should be either washed with gasoline or 
benzine, or be rubbed with finely powdered chalk, taking care to 
remove all of the chalk before trying to ink again, as it will clog 
the pen. It may be washed with gasoline or benzine to remove 
pencil marks or smudge after the drawing is finished, without 
affecting the ink. 

Tracing cloth is affected by the moisture of the air which 
causes it to stretch, and water will ruin it. 


[ 10 ] 


14. Blue Print Paper is made of several different grades of 
white paper covered with a coating sensitive to light. In print¬ 
ing, the inked side of the tracing should be placed next the glass 
in the frame or machine, and then the sensitive side of the paper 
next the tracing. They are held tightly in this position by a 
board or cloth, and exposed to a bright light for a time, depend¬ 
ing on the “speed” of the paper. That part of the coating 
protected from the light by the lines on the tracing is washed 
away when the print is placed in water while the exposed 
portions turn blue; hence the result is white lines on a blue 
ground. These prints may be mounted on a smooth flat surface 
and given a coat of schellac thus forming very durable shop 
drawings. 


CHAPTER 2 


LETTERING 


15. Proportion. One of the essentials to good lettering is 
a thorough understanding of the relative proportions of the dif¬ 
ferent parts of each letter. The letters should be studied indi¬ 
vidually with a view to resolving each into its fundamentals. 
Space will not permit a detailed discussion of this subject here, 
but with one or two examples by way of suggestion the student 
will be able to analyse the letters and numerals for himself, and 
thus fix in his mind the relation of the component parts. 

Refer to sheet 200, page 14. Note that each letter and nu¬ 
meral is placed in a square. The A for example is just a little 
wider than the square, or in other words is a trifle wider than it 
is high. The inclined strokes make equal angles with the hori¬ 
zontal. The horizontal bar is about one-third of the height of 
the letter above the lower guide line. 

The S is composed of parts of two ovals, one larger than the 
other. If they were completed the result would be something 
like a figure 8. The extreme width of the letter is somewhat less 
than its height. At the right the lower loop extends a little be¬ 
yond the end of the stroke above. At the left the vertical line 
touches the end of the stroke of the lower loop, and is tangent 
to the upper loop. The direction of the stroke is exactly hori¬ 
zontal at the point of reversal of curvature a little above the cen¬ 
ter line of the space. 

16. Forming’. In forming the letters it is necessary to di¬ 
vide each into parts which can be made with one stroke of the 
pen. Some of the strokes are natural divisions while others are 
arranged arbitrarily according to convenience. It is essential 


from the standpoint of time saving and to gain uniformity in 
rendering that each letter have a fixed number of strokes, and 
that they always be made in the same order and in the same di¬ 
rection. 

Hence, besides keeping the proportions of the letters in mind, 
there are three other points of prime importance,—order, num¬ 
ber and direction of strokes. For the details of this system see 
Phillips’ Freehand Lettering. 

In the case of the upright Gothic capitals it will be noted that 
in general all horizontal strokes are made from left to right, and 
that all vertical and straight inclined strokes are made down¬ 
ward. 

17. Spacing’. Next in importance to the correct forming of 
letters is their spacing in words. Owing to the great variety of 
combinations it would be impossible to make any very definite 
rules regarding spacing in general. It must be done largely by 
eye. In order to have a working basis for this estimate the fol¬ 
lowing is suggested. There are three combinations of contours 
that may be easily reduced to rule, by making the area included 
between them always equal. In this discussion one-half of the 
width of the H is taken as the unit space. 

(а) Case 1. When the letters have adjacent parallel strokes. 
In this case the space between the adjacent strokes is the full 
unit of space. Fig. 7. 

(б) Case 2. When a curved contour like that of the 0 is ad¬ 
jacent to a full length straight stroke. In this case the clear 
distance between the letters is less than the full unit of space. 



Make the area included between the contours equal to that in 
the rectangle of the unit space. This can be done by drawing 
in, or imagining drawn in, a space line as a, b., Fig. 7, and 




a 

c 

e 







_ 

W — 






b 

d 

f 


Fig. 7 

drawing the curve in such a way that the blackened area inside 
the curve will balance those outside. This may be termed the 
medium space. 

(c) Case 3. When the adjacent contours are both convex 
curves. In this case the clear distance between the letters is 
decidedly less than the unit space. Here again the space lines 
may be drawn as cd and ef, Fig. 7, and the same reasoning 
employed as before to make the included area equal to that of 
the unit space rectangle. This may be termed minimum spac¬ 
ing. 

{d) Case 4. When the adjacent contours are irregular and 
cannot therefore be classified in any of the other groups. No 
rule can be given. The spacing should appear uniform with 
that of cases 1, 2 and 3. 

18. Space Between Words. The unit of space between 
words is one and one-half the width of the H or three times that 
between letters. 

19. Titles. The relative importance of the various items of 
the title is shown by their arrangement and the character of the 
letters in which they are printed. 

(a) Balancing the Title. A title of two or more lines should 
be arranged so that the middle point of each line is on the same 
vertical straight line. The title is then said to be balanced. To 
balance the title each line should first be lettered on a scrap of 
paper, taking care to make it accurate in height and to space 


the letters correctly. Each line should be complete in itself, but 
it need not have any definite relation to the other lines at this 
stage. Mark the middle point of each line and cut out strips of 
paper containing the lines. Fig. 8 A. Draw pencil guide lines 
on the sheet according to the layout given. Select the strip 
containing the longest line of the title and lay it above its 
space on the sheet with one end of the line one-half inch from 



the right border line. Fig. 8 B. Mark the middle point on the 
sheet and draw a vertical line through it. This will be the 
center line of the title. The printed lines may now be laid 
above the spaces with their middle points on the center line and 
lettered according to the spacing on the trial slip. 

20. Notes. All notes on the drawing should be printed in 
Upright Gothic capitals high in Course 1, and in Inclined 
Gothic lower case high in Course 2. 














































21. Lettering 1 Practice. A few minutes at the beginning 
of each period is devoted to an analysis of a small group of let¬ 
ters. This is followed by practice in forming those letters. The 
materials used are tracing cloth on which guide lines have been 
ruled with a soft pencil, writing pen and and black ink. 

For this purpose the work has been divided into lessons as 
follows: 

(a) Course 1. Vertical Capitals. 

Lesson 1—I, L, T. 

Lesson 2—H, F, E. 

Lesson 3—Z, N, M. 

Lesson 4—A, V, W. 

Lesson 5—K, X, Y. 

Lesson 6—U, J. 

Lesson 7—O, Q. C. 

Lesson 8—G, D. 

Lesson 9—P, R, B. 

Lesson 10—S and any other letter which has been difficult for 
the student. 

Lesson 11—1, 4, 7. 

Lesson 12—2, 5, 3. 

Lesson 13—0, 6, 9. 

Lesson 14—8 and any other numeral which has been difficult 
for the student. 

Lesson 15—Spacing—General plan—Case 1. Page 9. 


Lesson 16—Spacing. Case 2. Page 9. 

Lesson 17—Spacing. Case 3. Page 10. 

Lesson 18—Spacing—Irregular letters. Consider the follow¬ 
ing combinations: L T; FE; AVW; KXYZ; JCG; RBS. 
Lesson 19—Spacing—LAKE; VALVE; PROJECTIONS. 
Lesson 20—Spacing—Sentence work. 

(b) Course 2. Inclined Lower Case. 

Lesson 1—1, i, t. 

Lesson 2—z, v, w. 

Lesson 3—x, y, k. 

Lesson 4—j, f. 

Lesson 5—r, h, n, m. 

Lesson 6—u. 

Lesson 7—o, c, e. 

Lesson 8—a, d, q, g. 

Lesson 9—b, p, s. 

Lesson 10—1, 4, 7. 

Lesson 11—2, 5, 3. 

Lesson 12—0, 6, 9. 

Lesson 13—8. 

Lesson 14—Spacing—Case 1—Page 9. 

Lesson 15—Spacing—Case 2—Page 9. 

Lesson 16—Spacing—Case 3—Page 10. 

Lesson 17—Spacing—Irregular letters. 

Lesson 18—Spacing—Sentence work. 


PLATE I 

UPRIGHT GOTHIC LETTERS AND FIGURES 


The student should be thoroughly familiar with the subject 
matter of the following references before attempting this plate: 
Arts. 3, 4, 5, 7, and 15. 

Size of Plates. The finished plates are ll"xl5"; the rect¬ 
angular area enclosed by the border line is 10"xl4", thus pro¬ 
viding a space between the border line and the edges of the 
plate. The border line when drawn in pencil is a good, sharp, 
clean-cut line. In fastening the paper to the drawing-board— 
if the sheet is previously cut to about 11" x 15"—the thumb tacks 
should pierce the paper *" from each of the two edges. Upon 
removal from the board, the thumb tack holes should be closed 
by pressing back into place the paper disturbed by the tacks. If 
the sheet is larger than ll"xl5", the tack holes should not show 
in the finished plate. 

Starting 1 the Work. Fasten the paper (one sheet only) to 
the board by means of thumb tacks, one in each corner, pressed 
down until the heads are flush with the paper. Insert a tack in 
one corner, make the paper square with the board by means of 
the T-square, stretch it diagonally across to the other corner and 
insert a second tack; stretch the paper diagonally in the other 
direction and insert tacks. It is essential to have the paper 
stretched flat. With large sheets it may be necessary to insert 
additional tacks along the edges. A tack may be temporarily 
removed when it interferes with the work. 

To Lay out the Border Lines and Guide Lines. Layout the 
10" x 14" border line as follows: Working from the upper left 
hand corner of the sheet measure down \ from the same cor¬ 
ner measure to the right. Draw a horizontal line through 
the first point and a vertical line through the second, thus loca¬ 
ting two sides of the 10" x 14" rectangle. From the upper left 


hand corner of the border line lay off 14" to the right and 10 /r 
down, and through the points thus located draw the remaining 
sides of the rectangle. 

Layout the guide lines for the plate according to sheet 201 in 
very light pencil lines. Place the letters and numerals as shown 
in sheet 200, each letter occupying a square. Immediately fol¬ 
lowing each letter is a smaller letter in height. Each small 
letter or numeral is spaced from the large one as at Aa unless 
otherwise indicated. 

Note the proportions of each letter and numeral, comparing 
carefully its width and height with the square in which it is 
drawn. All letters and numerals are made with a single weight 
pencil line. The pencil should be sharpened frequently to in¬ 
sure fine, clear-cut lines. Use a 3H pencil for all free hand 
work. 

Title. In the lower right hand corner of the sheet rule guide 
lines according to the dimensions given in the layout in sheet 
201. The longest line should end from the right border line, 
as shown. The space between any two of the longer lines of a 
title is not less than the height of the adjacent letters. The title 
as a whole should be arranged so that a verticle line through the 
middle of one line will bisect every other line. See Art. 19a, 
for the method of balancing a title. 

In the first line of the title letter the words “Upright Gothic” 
and in the second line the words “letters and figures.’’ 

The Filing 1 Circle and its horizontal diameter are drawn as 
shown on sheet 201. The sheet number, plate number, filing 
number and students’ initials are placed as shown. These 
three lines of figures and initials are symmetrical with regard to 
an imaginary vertical line through the center of the filing circle. 



[15] 























































































































































































































































HHnOHE 




nHnHHDHDH 



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UNIVERSITY OF WISCONSIN 
DEPARTMENT OF DRAWING 
COURSE I 


[ 16 ] 




























































































CHAPTER 3 


WORKING DRAWINGS 

WORKING METHODS - CONVENTIONS - DIMENSIONING 


22. Speed. Accuracy, and Neatness. The requisites for 
a good draftsman are speed, accuracy, and neatness. The good 
draftsman combines accuracy and speed by a judicious handling 
of the instruments and a studied method of procedure. He does 
things in the most economical order. He looks ahead as far as 
possible and groups like operations so as to avoid unnecessary 
handling and adjustment of instruments. As far as possible 
all circles of the same radius are drawn while the compass is in 
the hand; all possiblemeasurements are laid off from the seale at 
one time, etc. 

All straight edges, angles, scales, etc., should be carefully 
tested, joints of instruments kept in good order and their points 
sharp; then by careful handling, fine lines and points in their 
proper positions may be secured in the drawing. The time used 
in sharpening pencils and keeping the instruments in good order 
is well spent. 

Errors multiply with the number of operations involved, so 
other things being equal, the most direct construction is the 
most accurate. The location of points by very oblique intersec¬ 
tions should be avoided. 

The student should always sacrifice time to accuracy; speed 
will obtain through practice. 

To secure neatness, the instruments should be kept clean, and 
in good working condition, and blotting and erasing should be 
avoided. Orderly habits aid greatly in securing neatness of 
work. 


23. Starting’ the Work, The first thing in order is to fasten 
the paper on the board. This is best accomplished by inserting 
a tack in the upper left hand corner, squaring it on the board 
with the T-square against the lower edge, and then stretching it 
diagonally across to the other corner and inserting a second 
tack; now stretch it diagonally the other way and fasten as be¬ 
fore. This method of procedure will insure the paper being 
stretched smooth and flat. 

It will be found awkward to use the T-square near the lower 
edge of the board, and hence when the paper is smaller than the 
board it should be placed well above the lower edge. 

Having placed the paper on the board lay off a rectaugular 
border line according to the size of the plate to be made, allowing 
space along all four sides so that the drawing may be trimmed 
with a margin on all sides outside of the border line. Do not 
assume that the paper is cut to the proper size and measure in 

on all sides, but start at one corner and lay off the sides of 
the rectangle with the scale. 

24. Planning the Drawing. In deciding the scale of a 
drawing the draftsman must consider not only his convenience 
in drawing the views on the sheet, but also the use to which the 
drawing is to be put. It should not be of such a size as to be 
unwieldly to the mechanic nor small enough to be confusing. 

(a) Number, Kind and Arrangement of Vieivs. The number 
of views is determined by what the draftsman’s judgment tells 
him makes the drawing thoroughly intelligible to the mechanic. 


[ 17 ] 



All necessary views and no more should be given. Select 
views that show the object in the most comprehensive manner. 
Sectional views often make the inside of an object clearer to the 
mechanic. 



The views must always have a fixed relation to each other ac¬ 
cording to the rules of third angle projection. 

(6) Location of Views with Reference to Each Other. The dis¬ 
tance between views of an object should be as small as possible 
and still have each view stand out as a distinct view. For the 



Fig. 10 


problems of this course the distance between views should as a 
rule be not less than f" nor more than 1". 

(c) The Enclosing Rectangle. The rectangle in which the 
views are inscribed is known as the enclosing rectangle. The 
dimensions of the enclosing rectangle are determined for two 
views as follows: Fig. 9. A the width of the rectangle 
equals a plus b plus c. B, the height of the rectangle equals B. 
When three views are required, Fig. 10, A equals a plus b plus 
c and B equals d plus b plus e. A small freehand trial sketch 



should be made for the purpose of determining the size of the 
enclosing rectangle for the required group of views. In some 
cases consideration is given to the dimensions to be placed on 
the several views in determining the size of the enclosing rec¬ 
tangle. In this course the several views are to be accurately 
balanced on the sheet according to the instructions here given. 

(d) Location of the Drawing Within the Border Line. The 
required group of views is located within the border line by de¬ 
termining the position of the enclosing rectangle. It should be 
located so that m equals m and n equals n or what is the same 
thing B plus (2 x n) equals 10" and A plus (2 x m) equals 
14". Fig 11. 


[ 18 ] 



































































25. Working 1 Methods. From what has already been said 
about speed and accuracy, the need of going about the work 
systematically is easily recognized. The system reduces to what 
is usually termed “drawing by stages.” 

(a) Constructive Stage. Under this head comes the laying out 
of the drawing and all instrumental penciling. In this stage all 
lines should be made light and full, no dotted lines being used 
at all. As hard a pencil should be used as the paper will per¬ 
mit. Lines may be drawn longer than absolutely necessary to 



avoid the possibility of having to patch them. Do not erase 
until the drawing is finished. See sheet 204. 

Centers for rounded corners, fillets and other arcs which do 
not have their centers on any line of the drawing are located 
by what is called the “trial and error” method. First adjust 
the compass to the proper radius, then set the lead on the tangent 
line at a making a c as nearly as possible equal to the radius 
(by eye). Set the needle point opposite a and bring the lead 
around to d. Move the needle point parallel to a c an amount 
equal to the error. 

To insure accuracy the points of tangency are now located 
exactly by the method illustrated in Fig. 13. A triangle a is 


placed with its edge along the tangent line as shown in dotted 
lines, a second triangle b is placed against the first and held 
stationary while the first is revolved into the second position in 
which one edge is perpendicular to the tangent line and passes 
through the center of the arc. According to the laws of geometry 
the foot of the radius perpendicular to the tangent line is the 
point of tangency. The point of tangency should be located 
by a short mark as shown at c. The lines mrking the points 
a of tangency should be left as a guide in inking but should 
not be traced. 

(5) Finishing Stage. Go over all the lines, making them 
heavier and ending them at the proper points. Render all con¬ 
ventions. Dotted lines may now be made where required, going 
over the light full lines but do not try to erase between the 
dashes. The dashes should be all of the same length and the 
ends well defined. Put in extension and dimension lines, and 
dimensions, also notes and the title. 

(c) Inking is the last stage of the drawing and may be itself 
divided into stages. It includes the rendering of dimensions 
and lettering, which should come after the instrumental inking. 
Care should be taken to keeep all lines of the same class of a 
uniform width. Particular attention should be given in dotted 
lines to make all dashes the same length , with both ends square 
and the spaces equal. Where lines meet they should run into 
each other, neithr falling short nor running over. All corners 
should be perfect. 

The work of inking may be divided into steps as follows, be¬ 
ginning at the upper left hand corner and working downward 
and to the right: (1) Draw all circles and arcs, the smaller 
ones first and all of the same radius at one setting of the Com¬ 
pass. (2) Ink vertical lines. (3) Ink all horizontal and other 
straight lines. (4) Render the dimensions. (5) Put in screw 
thread conventions, show breaks, and cross hatch sections. (6) 
Put in the title and ink the border line. 

26. Erasure. Many students find trouble in erasing from 
the tracing cloth without maring the drawing. If proper care 






is taken ink may be erased so that the surface of the cloth is 
hardly affected. A shield of brass or celluloid should be used 
and the opening in it which best fits the line or spot to be erased 
selected. By holding it firmly with the fingers of the left hand 
and employing an ordinary pencil eraser in the right, the ink 
will readily yield. Finish by polishing with a smooth surface 
such as the thumb nail, a piece of ivory or soapstone. 



Fig. 14 


27. Conventions, (a) Lines. Fig. 14. A drawing in or¬ 
der to be clear and legible must have the different ideas involved 
expressed by characteristic lines. Furthermore it is very essen¬ 
tial to the good appearance of the drawing that each class of 
lines be uniform in width, density and execution. 

(&) Object Lines. The full lines in ink depend somewhat on 
the size of the drawing, but ordinarily they should be about 
oV' in width." 

(c) Invisible Lines. Lines representing hidden edges are 
dash lines, about the same weight as the object line, dashes i" 


and spaces -g?" long. Caution—Dotted lines when ruled with 
the same setting of the pen as the object lines often appear 
heavier than the object line due to the frequent starting and 
stopping of the flow of ink. Especially is this true if the pen 
is very full. In this case the width of the dotted line should be 
slightly reduced. For methods of joining lines, see A and B, 
Fig. 14. 

Use as few dotted lines as clearness will permit, 

(d) Center Lines. A center line is used to indicate a natural 
axis of symmetry. A main center line is one about which the 
object or view as a whole is symmetrical, while a secondary 
center line is an axis of symmetry for part only of a view or ob¬ 
ject. The main center lines should extend about beyond the 
outline of the view and the secondary center line somewhat less. 
Every circle has two center lines at right angles. 

Center lines may be circular as in the case of a group of 
holes arranged on the circumference of a circle. The center line 
is not quite a complete circle. They may also be radial lines, 
as in the above case, where the other center lines of the holes 
are radial lines from the center of the circular center line. They 
are full black lines and about \ the weight of the object line or 
X 2 ¥ in- in width. 

(e) Dimension and Extension Lines. Dimension lines indi¬ 
cate dimensions between certain limits. A full red line is used 
of the same weight as the center line. It should be broken at 
some point, preferably the middle, to allow putting in the dimen¬ 
sion. In general, arrow heads are placed one at each end. 

A radius dimension should have an arrow only at the arc. 
A small circle in black should enclose the center from which it 
is drawn. 

When a dimension is placed off the view, parallel lines are 
extended from the points between which it is to be shown, and 
the dimension line placed between and at right angles to them. 
They should begin -fc" from the object line of which they are a 
continuation and end beyond the arrow head. 

(/) Broken Lines. Where it is desired to show a broken 


0 ] 






































edge a ragged line is drawn, with a writing pen, of about the 
same weight as the object line. 

( g) Border Line. The border line should be a heavy black 
line v in width. 

(h) Doubtful Lines. A rounded or fileted corner, or other 
curved surface which theoretically cannot be represented by a 
line should be so represented where it adds clearness to the 
drawing. 

( i) Arrow lJpads are black, about long. They must be 
made freehand with a common writing pen. They should be 
very slender, hugging the dimension line closely, the barbs be¬ 
ing slightly curved coming in tangent to the dimension line at 
its end. See C, Fig. 14. 

O') Finish Marlts. Surfaces to be finished may be marked 
by placing a small f crossing the line representing the surface,, 
it being itself crossed on the line. The mark is omitted when 
the finish is otherwise denoted, as by a note 3" Bore, 2" Turn, 
etc. When all the surfaces are to be finished a note is made 
FINISH ALL OVER, or the word FINISHED placed in the title. 

(k) Sectioning. The drawing can often be made much clearer 
and simpler by supposing the object cut by a plane and a por¬ 
tion removed. One of the chief advantages is the reduction in 
the number of dotted lines which become confusing, when a 
number are necessary. Sections are usually taken by passing a 
plane through an axis of symmetry and parallel to one of the 
planes of projection. If by this process the object is divided 
into two similar parts the drawing is termed a half section. When 
the object is symmetrical it is often better to make a combined 
outside and sectional view, the division usually being made at 
the center line. If the two section planes are taken at right 
angles to each other, cutting to the axis of the object, the-draw¬ 
ing is termed a quarter section. 

The supposedly cut surface is conventionally represented by 
what is called cross-hatching, which consists of very fine paral¬ 
lel lines equally spaced and inclined to the horizontal. When 
an object consists of more than one part, adjacent surfaces be¬ 


longing to the different parts are distinguished by sloping the 
lines to right and left respectively. 

Different metals and materials may be characterized by adopt¬ 
ing characteristic lines, spacing and inclinations, in the hatch¬ 
ing. The most common one, cast iron, is represented by a fine 
full line about center line weight inclined at 45° and spaced ac¬ 
cording to the size of the surface. An average spacing is about 
tv". The spacing is done entirely by the eye. The student 
should practice on a scrap of paper so as to learn to judge the 
spaces correctly before attempting to work on a drawing. Un¬ 
less he is very careful he will find the width of spaces changing 



as he proceeds, and in order to overcome that difficulty he 
should keep constantly comparing the one he is drawing with 
the first ones drawn. A common method is to estimate the dis¬ 
tance, b, Fig. 15, the ruling edge of the last line drawn, in 
doing which it is necessary to make allowance for the space 
taken up by the pen or pencil, thus introducing another factor 
of error. This may be avoided by holding the pen or pencil in 
position against the ruling edge so that it doesn’t quite touch 
the cloth or paper, and judging the space a from the last line 
drawn to the point of the pen or pencil. It is a process 
requiring considerable care and should not be hurried or 
slighted in any way, the usual penalty for which, coming as 
it does in the finishing stage of the drawing, is a rather trouble¬ 
some erasure at least. 


[ 21 ] 





(1) Screw Threads are based on the curve which is known as 
the helix, Pig. 16, A. It is generated.by a point which moves on 
the surface of a cylinder with a uniform motion parallel to the 
axis and at the same time rotates about the axis with a uniform 
motion. The distance traversed by a point parallel to the axis 
in one revolution is called the pitch. In the case of thread this 







C4 — 



1 - 




I - 




o - 


! y 



1 



Ol 

! j -ssr: 



1 




- 

- 



I 

( 





A 


B 

Fig. 16 






is the distance measured parallel to the axis between correspond¬ 
ing points on two successive threads. 

Square Thread Fig. 16 B, shows the projection of a right 
square thread. Fig 16 C, shows the conventional representation 
of a right square thread where the curves are replaced by 
straight lines. 

Y Thread. Fig. 17 A, is the projection of a V thread. B 
and C, Fig. 17, are conventional representations of the V thread. 
B is sometimes used when the drawing is made to large scale or 
for exhibition purposes, but C is used in common practice. C 



Fig. 17 




[ 22 ] 


Fig. 18 















































































is arrived at by first making the curved lines straight and then 
omitting the short lines forming the saw edge. 

The Pipe Thread is illustrated in Fig 18. In order to insure 
tight joints the threaded portion tapers as shown. The first four 



threads at the left (sectional portion), are imperfect at the top 
and root, the next two are imperfect at the top only, and all to 
the right of these are full threads. 

Bolts. Fig. 19, A and B, give the proportions for drawing 
hexagonal head and square head bolts. These proportions do 


not correspond to the actual dimensions. See a table^of bolt and 
nut sizes for actual sizes. 

A Stud. Fig. 20 A, is a rod of metal threaded at both ends, 
and is used for fastening on such things as cylinder heads. The 
figure illustrates the method of its application. 

A Cap Screw. Fig. 20 B, is a rod of metal with a head at 
one end and threaded at the other for about two-thirds of its 
length. 

Machine Screws are similar to cap screws, and are used for 




A 0 

Fig. 20 


C 


like purposes, but usually for smaller work. The main point of 
difference is that cap screws are measured in inches, while ma¬ 
chine screws are designated by a machine screw gage. Both have 
heads of various shapes. 

Set Screw. Fig. 20 C, shows a set screw. Its function is 
to prevent relative motion of the two parts which are held in 
contact by some other means, as, for instance, a shaft in the hub 
of a pulley. 

Methods of representing the side, section and end views of 
tapped holes and bolts are shown at B and C, Fig. 21. These 













































































should be carefully studied and kept in mind for future use. 
Note that the inclination of the threads in the section of the 
tapped hole is opposite to that of the bolt which fits it. 

28. Dimensioning’. Possibly more here than anywhere in 
the drawing is the draftsman’s best judgment called into play. 
It is absolutely necessary to avoid mistakes, and to facilitate the 
work of the mechanic, that the necessary dimensions only be given, 
and those placed in such a way as to make the drawing easily 



ABC 

Fig. 21 


read and interpreted. Placing of dimensions in obscure and 
unexpected places should be avoided, and where ever possible 
they should be grouped in such a manner that their relation to 
each other is obvious. No doubt the best guide to follow is for 
the draftsman to imagine himself in the mechanic’s place and 
consider the operations the object must go through in order to 
become a finished product. With this idea in mind, and a 
working knowledge of shop methods, which every draftsman 
should possess, many of the problems will be readily solved. 
To illustrate, when the machinist drills a hole he sets the point 


of the drill at the center, and hence the hole should be dimen¬ 
sioned by referring its center to some surface, line or point, 
easily accessible. 

(a) Form. The general form of the dimension includes the 
extension and dimension lines, numerals and arrow heads. 

(&) To Read. All dimensions should read from the lower 
and right hand edges of the drawing. 

(c) Notation. Feet and inches are denoted by the signs ' and 
" respectively, thus 5'-6" (not 5 ft. 6 ins). 

( d) Denomination. Dimensions up to 2' are given in inches 
and all above in feet and inches, thus 23|", 2'-4". 



Fig. 22 


(e) Fractions. Conventional fractions are used having de¬ 
nominators as shown, i, I, iV, ti- Do not use such frac¬ 
tions as tV> tV* etc. For very accurate dimensions such as clear¬ 
ance, special fits, etc., decimals are used and are written thus, 
5" + 0.006", 3" - 0.0025". 

(/) Height of Numerals and Fractions. Use plain vertical 
figures 3 V" high, the numerals in both the numerator and denom¬ 
inator of the fraction being each high, or the same as the 
whole number. Leave a small space between the numerals and 
division line of the fraction. This adds greatly to the neat ap¬ 
pearance. 

( g) The Scale of the drawing should be placed under the title 
and written thus, Scale Full Size, Scale Half Size. 

(Ji) Arrangement. Do not give the same dimension twice, 
nor leave them so that the workman has any calculating to do. 

[ 24 ] 



































Judgment must be exercised in placing dimensions on or off 
the views. In general use the method which insures clearness. 

When dimensions are grouped in parallel lines they should be 
graded from the shortest on the inside to the longest outside, 
Pig. 22. This arrangement avoids crossing of dimension lines 
by extension lines which is confusing. 

Cross-hatching should be broken to allow space for numerals 
but not for the dimension line, Fig. 22. 

(«') Diametral Dimensions. Circles should be dimensioned on 
their diameters when possible, but never on a center line, Fig. 
23. When there is not room inside the circle to place the figures 




extension lines may be drawn out from the ends of a diameter 
and the figures placed outside. In case it is deemed advisable 
to place the diameter between parallel lines, as in the case of 
the side view of a cylinder, note should be made of the fact by 
placing DIA. or D. after the dimension. 

( j ) Radii. Where there is room the dimensions should be 
placed between the center and the arc. If for any reason the 
space is cramped, or in case of a cross-hatched surface with a 
rounded corner, the center may be ignored and the dimension 
placed as shown in Fig. 24. The notation R or RAD. should 
be added. In case of arcs of large radius where the center is 
inaccessible dimension as shown. 


( k) Small Parts. For various methods of dimensioning small 
parts where there is not room to place the figures or arrow heads, 
or both between the extension lines, see Fig. 22. 

{1) Drilled , Gored or Tapped Holes. A hole to be drilled, 
cored or tapped is dimensioned conventionally by placing, in a 



Fig. 24 


convenient space near the hole, the figures expressing its diame¬ 
ter followed by the word Drill, Core or Tap and underlined by 
a line which is bent if necesserv and terminated by an arrow 
inside the circle. See Fig. 21 A. 

When holes of the same size are symmetricaly grouped, upon 
which the same operation is to be performed, they are dimen¬ 



sioned by what is termed a blanket note such as, Core 8 Holes 
¥' DIA. Drill 16 Holes l" DIA., 8 Holes f" Tap, If' Deep. 

{m) Angles are dimensioned as shown in Fig. 25. The dimen¬ 
sion lines are arcs with center at the vertex of the angle. 


[ 25 ] 



















PLATE 2 

EXERCISES WITH TRIANGLES, T-SQUARE AND PENCIL 


Read all the following directions before beginning to draw; 
while the drawing is being made, read each reference as it occurs 
in the directions. 

Make a complete pencil drawing of sheet No. 202. 

Figure 1. Sheet 202. Draw a horizontal center line for 
the sheet and on this center line measure 4" to the right from 
the left border line. This will locate the center of Figure 1. 
Through this point, using the triangle against the T-square, and 
the wedge-shaped lead of the pencil, draw E F perpendicular to 
the horizontal line. With the 45° triangle against the T-square 
draw A B. See Art. 4b. All lines should be drawn very light, 
no attempt being made to draw them of definite length. They 
may be gone over afterward, made more distinct and of the 
proper lengths. See Art. 25 a and b. With the scale and the 
sharp conical point of the pencil lay off 2" on each side of the 
center on A B. Through these points draw C E and F I) per¬ 
pendicular to A B. These lines will also be at 45° to the hori¬ 
zontal. Through the points where C E and F D strike the hori¬ 
zontal and vertical lines, draw E D and C F at 45° to the hori¬ 
zontal and parallel to A B. 

On all four sides of the square thus formed lay off spaces 
with the scale and sharp conical point of the pencil. In the tri¬ 
angles formed by the diagonals of the square and its sides draw 
alternate full and dotted lines as shown. All lines should be 


full and very light at first. Those that are to be dotted will be 
made so when the lines are gone over. Omit all letters and 
dimensions from the finished plate. 

Figure 2. Sheet 202. Locate the center of Figure 2 as 
shown. Draw L M at 30° and O N at 60° to the horizontal. 
Draw P Q at 75° to the horizontal and on it mark points 2" on 
each side on the center of the figure. Through these points 
draw L N and O M, perpendicular to P Q, or what is the same 
thing at 15° to the horizontal. Through the points where these 
lines strike the 30° to 60° lines draw lines parallel to P Q (at 
75° to the horizontal.) Lay off 1" spaces on all four sides of 
the square thus formed. In the triangles formed by the sides of 
the square and its diagonals, draw alternate full and dotted 
lines, as shown. 

Draw the filing circle in the lower left hand corner of the 
sheet and letter therein the appropriate sheet number, plate 
number, and filing number. Add the initials below the filing 
circle, keeping the lines of figures and letters symmetrical with 
reference to an imaginary vertical line through the center. 

Title. Letter the word “Exercises’ ’ in the lower right hand 
corner of the sheet, i" above the border, and from the right 
border line. The letters should be . in height. 

Refer constantly to the lettering pamphlet when making the let¬ 
ters and numerals in the above. 


[ 26 ] 




[27] 
























PLATE 3 

EXERCISES WITH THE TRIANGLES, T-SQUARE AND RULING PEN 


Make a complete tracing of Plate 2. 

Read all the following references beginning before to draw. 
Arts. 11, 13, 25e, 26. 

To Stretch the Tracing 1 Cloth. Use the dull side of the 
tracing cloth. It is cut slightly larger than the drawing 
paper and the greater part of the extra area is to be left 
at the top and right hand sides. This extra area is used 
to try the pens on, before inking in the work. Remove the lower 
left hand tack from the drawing. Place the tracing cloth over 
the drawing so that it extends about i" beyond the lower and left 
hand edges of the paper. Insert the tack into the hole that it 
previously occupied. Remove the tack from the upper right 
hand corner of the sheet. Stretch the tracing cloth diagonally, 
and insert the tack as before. Proceed in a similar manner with 
the other two corners. The tracing cloth should lay flat on the 
drawing paper. If tracing cloth is allowed to remain on the 
board some time its surface becomes uneven on account of 
changes in the atmosphere. If the cloth becomes uneven it should 
be restretched as described above. The tracing cloth should not 
be fastened over the drawing until the tracing is to be started. 


Preliminary Practice. It is good practice to ink the squares, 
rectangles and triangles until not only the lines are good,' but 
the corners and intersections as well. Corners should be very 
definite. Be careful to stop each line at exactly the right point, 
for ragged corners and poor intersections indicate careless work. 

Use only Mach ink for this plate. 

Pencil Guide Lines. The student should rule guide lines for 
all lettering, using a 3H pencil. Guide lines ruled on the draw¬ 
ing paper will not answer when lettering on the tracing cloth. 
Ruling the guide lines on the surface to be lettered gives better 
results. 

The tracing cloth should be carefully cleaned with a soft 
rubber in order to remove all pencil and other marks before 
blue printing. A hard eraser should not be used for clean¬ 
ing purposes as it will remove the ink from the lines of the 
drawing. 

To Cut the Tracing 1 Cloth to the required size, after the 
drawing is completed, use a very sharp knife. The working 
edge of the T-square should dot be used to guide the knife. 


[ 28 ] 


PLATE 4 

EXERCISES WITH COMPASS AND BOW PENCIL 


Read the following references before beginning to draw. Arts. 
8 and 10. 

Make a complete pencil drawing of Sheet No. 203. 

Penciling 1 . In making dashed lines with the compass the lead 
should be sharpened to a conical point in order that the ends of 
the dashes may be made distinct. All dimensions, dimension 
lines, numerals and letters, except those in the title and filing 
corner of the plate, should be omitted. 

Figure 1, Sheet 203. Locate the center of the figure as 
shown. With the scale and a very sharp pencil, mark off the 
given distances on the radius A. Note. Insert a piece of 
“4H” lead in the pencil leg of the compass. The leads sold with 
the instruments are too soft. Draw the smallest circle first, draw¬ 


ing the dashed circles as shown. Keep the compass pencil lead 
sharp. 

Figure 2, Sheet 203. Insert the lengthening bar in the 
compass, and with the center at B describe arcs as shown. Draw 
the filing circle in the lower left hand corner of the sheet, and 
letter therein the appropriate sheet number, plate number, and 
filing number. Add the initials below the filing circle, keeping 
the lines of figures and letters symmetrical with reference to an 
imaginary vertical line through the center. 

Title. Letter the word “Exercises’ 7 in the lower right hand 
corner of the sheet 1" above the lower border line and from 
the right border line. Refer constantly to the lettering pamphlet 
when making the letters and numerals for this plate. 


PLATE 5 

EXERCISES WITH THE COMPASS AND BOW PEN 

Make a complete tracing of Plate 4. Read the following ref¬ 
erences before beginning to draw. Art. 8d and 10. 

Use hlaclt ink for this plate. Practice with the compass and 
boiv pen before inking the required plate. 


r29] 



[30] 
























CHAPTER 4 


ORTHOGRAPHIC PROJECTION 


29. Let Fig. 26 represent a hollow cube with transparent 
laces. 

The top face is called the top plane. 

The front face is called the front plane. 

The right side face is called the right side plane. 

The left side face is called the left side plane. 



The right side view is the drawing of the object when viewed 
from the right side. 

The left side view is the drawing of the object when viewed 
from the left side. 



In Fig. 27 let the small cube (drawn heavy) be the object to 
be represented upon the faces of the large cube. 

The top view is the drawing of the object when viewed from 
above. 

The front view is the drawing of the object when viewed from 
in front. 


30. In orthographic projection every point of an object 
is viewed in a direction perpendicular to the faces of the cube. 

In Fig. 27 Aa is perpendicular to the top plane. 

Aa' is perpendicular to the front plane. 

Aa r/ is perpendicular to the side plane. 

In order that the views may be drawn in one plane the sur- 


[ 31 ] 































face upon which the drawing is made is conceived to be placed 
in contact with one of the planes of the cube as shown in Fig. 
28, then folded on edge of the cube into an adjacent face as 
shown in Fig. 29. 





Fig. 29 


[ 32 ] 


Fig. 31 































































In the same manner the top and right side views may be 
drawn as shown in Figs. 30 and 31. 

The two views of any point of the object are on a line per¬ 
pendicular to the edge on which the drawing was folded. 

© © 


® © 

a a' Fig. 29 is perpendicular to G L. 
a a" Fig. 31 is perpendicular to G" L". 

31. Points of the object are referred to by capital letters, 
A, B, C, etc. 

For points of the top view small letters are used, a, b, c., etc. 


For points of the front view small letters with the prime 
marks are used, a', b\ c', etc. 

For points of side and auxiliary views small letters with sec¬ 
ond marks are used, a", b // , c", etc. 


CONSTRUCTION OF POLYGONS 

32. 1. Fig. 32. 

Square. 

2. Fig. 33. 

Equilateral triangle. 

3. Fig. 34. 

Hexagon. 

4. Fig. 35. 

Octagon. 



Fig. 36 






[ 33 ] 




















PROBLEMS 


Problem. Fig. 36. Draw the top and front viefws of a 
regular square prism. Bases parallel to the top plane. Two 
opposite lateral faces parallel to the front plane. 

1. Top view. 

2. Front view. 

1. Draw the top and right sides views of a regular square 
prism. Bases parallel to the top plane. Two opposite lateral 
faces perpendicular to the side planes. 

2. Draw the front and left side views of a regular square 
prism. Bases parallel to the front plane. Two opposite lateral 
faces parallel to the side planes. 

3. Draw the front and right side views of a regular square 
prism. Bases parallel to the side planes. Two opposite lateral 
faces parallel to the front plane. 

4. Draw the left side and top views of a regular square 
prism. Bases parallel to the side planes. Two opposite lateral 
faces parallel to the top plane. 

Problem. Fig. 37. To draw the top and front views of a 
right circular cylinder. Bases parallel to the top plane. 

1. Top view. 

2. Front view. 

1. Draw the front and left side views of a right circular 
cylinder. Bases parallel to the front plane. 

2. Draw the front and right side views of a right circular cylin¬ 
der. Bases parallel to the side planes. 

3. Draw the left side and top views of a right circular cjdin- 
der. Bases parallel to the side planes. 

4. Draw the top and right side views of a right circular cylin¬ 
der. Bases parallel to the top plane. 

Problem. Fig. 38. To draw the top and front views of a reg¬ 
ular square pyramid. Base parallel to the top plane. Two op¬ 
posite edges of the base parallel to the front plane. Vertex 
above the base. 

1. Top view. 

2. Front view. 


1. Draw the top and left side views of a regular square pyra¬ 
mid. Base parallel to the top plane. Two opposite edges of 
the base perpendicular to the side planes. Vertex below the 
base. 

2. Draw the front and right side views of a regular square 
pyramid. Base parallel to the front plane. Two opposite edges 



Fig. 37 Fig. 38 


of the base parallel to the side planes. Vertex aboVe the base. 

3. Draw the right side and top views of a regular square 
pyramid. Base parallel to the side planes. Two opposite edges 
of the base perpendicular to the top plane. Vertex to the right 
of the base. 


[ 34 ] 





4. Draw the left side and front views of a regular square pyra¬ 
mid. Base parallel to the side planes. Two opposite edges of 
the base parallel to the front plane. Vertex to the right of the 
base. 

Problem. Fig. 39. To draw the top and front views of a 
right cone. Base parallel to the top plane. Vertex above the base. 



O 





Fig. 40 


1. Top view. 

2. Front view. 

1 . Draw the front and right side views of a right cone. Base 
parallel to the front plane. Vertex in front of the base. 

2. Draw the right side and top views of a right cone. Base 
parallel to the side planes. Vertex to the left of the base. 


3. Draw the top and left side views of a right cone. Base 
parallel to the top plane. Vertex to the left of the base. 

4. Draw the top and left side views of a right cone. Base 
parallel to the top plane. Vertex below the base. 

Problem. Fig. 40. To draw the top and front views of a 
sphere. 

Problem. Fig. 41. To draw the top, front and right side 
views of a regular hexagonal prism. Bases parallel to the side 
planes. Two opposite lateral faces parallel to the top plane. 



d 

c 


or 





1. Right side view. 

2. Front view. 

3. Top view. 

1 . Draw the top, front and left side views of a regular hex¬ 
agonal prism. Bases parallel to the front plane. Two opposite 
lateral faces parallel to the top plane. 


[ 35 ] 










2. Draw the top, front and right side views of a regular hex¬ 
agonal prism. Bases parallel to the top plane. Two opposite 
lateral faces perpendicular to the front plane. 




Fig. 42 



Problem. Fig. 42. To draw the top and front views of a 
regular square prism. Bases parallel to the top plane. Two op¬ 
posite lateral faces 15° with the front plane. 

1. Top view. 

2. Front view. 


1. Draw the left side and top views of a regular square 
prism. Bases parallel to the side planes. Two opposite lateral 
faces 30° with the top plane. 

2. Draw the front and right side views of a regular square 
prism. Bases parallel to the sides plane. Two opposite lateral 
faces 15° with the front plane. 

3. Draw the front [and left side views of a regular square 
prism. Bases parallel to the front plane. Two opposite lateral 
faces 60° with the side planes. 

4. Draw the top and right side views of a regular square 
prism. Bases parallel to the top plane. Two opposite lateral 
faces 30° degrees with side planes. 

Problem. Fig. 43. To draw the top and front views of a 
regular square pyramid. Base parallel to the top plane. 
Two opposite edges of the base 15° with the front plane. Ver¬ 
tex above the base. 

1. Top view. 

2. Front view. 

1. Draw the top and left side views of a regular square pyra¬ 
mid. Base parallel to the top plane. Two opposite edges of 
the base 60° with the side planes. Vertex below the base. 

2. Draw the front and right side views of a regular square 
pyramid. Base parallel to the front plane. Two opposite edges 
of the base 15° with the side planes. Vertex in front of the 
base. 

3. Draw the right side and top views of a regular square pyra¬ 
mid. Base parallel to the side planes. Two opposite edges of 
the base 30° with top plane. Vertex to the left of the base. 

4. Draw the left side and front views of a regular square pyra¬ 
mid. Base parallel to the side planes. Two opposite edges of 
the base 75° with the front plane. Vertex to the left of the 
base. 


[ 36 ] 









PLATE 6 

SHOP DRAWING IN PENCIL. SHEET 205. “PLANER CHUCK JAW” 


Given. The front view 1 and end view 2, of a “Planer 
Uhuck Jaw.” 

Draw. The front and left end views. Scale—Full size. 
Read all references as they occur. 

Use. The sketch represents a Planer Chuck Jaw. The chuck 
is bolted to the bed of the planer and holds the piece to be 
planed as in a vise. The Planer Chuck Jaw may be adjusted 
back and forth to accommodate the various sizes of the pieces to 
be planed. 

Analysis of Procedure. 

Lay out the border line. Art. 23. 

Lay out the enclosing rectangle. Art. 24a, b, c, d. 

Lay out the views very accurately with the sixteenth scale and 
draw very light lines of indefinite length (be sure they are long 
enough) as shown on Sheet 204. Art. 25a. 

Draw over the light lines making clear, firm lines ending them 
at the proper points and dotting hidden lines. 

Select carefully the dimensions that are necessary for the .me¬ 
chanic to have in order to make the piece, and arrange them so 
as to show their relation to each other in the clearest possible 
manner. Art. 28. All figures should [be A" high; those in 
the fractions as well as those in the whole number. Keep the 
lettering book open on the desk when putting in the figures, fol¬ 
lowing carefully the general form together with the order, num¬ 
ber and direction of strokes for each. 

The division line of the fraction should be in line with the di¬ 


mension line. The figures in numerator and denominator should 
not touch the division line. It is a good plan to draw the divi¬ 
sion line first in the fraction. All dimensions should read from 
the lower and right hand edges of the sheet. Arrowheads should 
be about long, the point touching the extension line. They 
should be very narrow, composed of two slightly curved lines 
and made with a fine writing pen. Art. 27i. 

The pencil should be sharpened often to secure the best re¬ 
sults. Use a 3H pencil for all freehand work. The student will 
in most cases need to give particular attention to the freehand 
work in order that it keep pace with the progress made in in¬ 
strumental execution. 

Extension lines should start ' from the object line and con¬ 
tinue ¥' beyond the arrowhead. Art. 27e. 

Title. Read Art. 19a. Lay out the guide lines for the title 
as given on sheet 204. Use the following material in the order 
given: 

PLANER CHUCK JAW 
1 WANTED-CAST IRON—FINISHED 
SCALE—FULL SIZE 

Print the sheet number and the plate number in the upper 
half of the filing circle and the filing number in the lower half 
as shown on Sheet 201. Print the initials below the filing circle 
so that they are balanced on the vertical center line of the filing 
circle. 


[ 37 ] 































PENCIL. LAYOUT — LINES ARE VERY LIGHT 








T 



[ 38 ] 






































UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE I 


[ 39 ] 




































PLATE 7 

TRACING OF PLATE 6 


Read carefully the general instructions for inking given. 
Arts 25e and lib. 

Ink on the dull side of the tracing cloth. All object lines 
should be black and Vi " in width. Art. 27b, c. Extension and 
dimension lines are red and one-half the weight of the object 
lines or (measured by eye). Art. 27e. Special care is neces¬ 
sary when using red ink as it dries quickly between the nibs. The 
variation in width of line, due to this cause, is especially notice¬ 


able when ruling fine lines. The pen should be frequently 
cleaned and refilled to secure the best results. 

All numerals and arrowheads are black. 

Freehand work should be practised on a scrap of tracing cloth 
before attempting the work on the required plate. Sample let¬ 
ters, figures and arrowheads should be submitted to the instruc¬ 
tor before inking the drawing. 


[ 40 ] 


PLATE 8 


SHOP DRAWING IN PENCIL. 

Note. The student’s drawing is to be made from the small 
sketch. Fig. 44. The drawing on sheet 206 is similar to the 
one the student is to make and is given to illustrate conventions, 
methods of dimensioning, etc. 



Given. The right side view 1 and back view 2 of a “Back 
Rest. w 

Draw. The front and left side views. Scale—Full size. 

Use. This piece and another similar to it form what is known 
as the back rest to a turrret lathe. The second piece is inverted 
and placed so that a 90° V is formed between the two. The re¬ 
volving rod, which is being turned rests in this V, and is thus 
prevented from being pushed out of true by the cutting tool. 


“TURRET LATHE BACK REST” 

Analysis of Procedure. 

Lay out the border line. Art. 23. 

Lay out the enclosing rectangle. Art. 24b, c, d. Make a 
small freehand sketch with over all dimensions to determine the 
size of the enclosing rectangle. The time thus employed will 
save many errors, and consequently considerable time in the 
end. 

Lay out the views very accurately with the sixteenth scale, 
and draw very light lines of indefinite length. (Be sure they 
are long enough.) Art. 25a. 

Draw over the light lines making clear, firm lines ending them 
at the proper points and dotting hidden lines. 

Select carefully the dimensions that are necessary for the me¬ 
chanic to have in order to make the piece, and arrange them so 
as to show their relation to each other in the clearest possible 
manner. Art. 28. 

Extreme care is necessary in all freehand work. All figures 
must be of the same height. Arrowheads should be neat and 
trim. The best results are obtained by making each stroke once 
and once only. Do not get into the habit of working over a 
letter two or three times. It is sure to produce an unpleasing 
effect. 

Study the lettering pamphlet while putting in letters and 
figures. 

Conventions. See Art. 28k for method of dimensioning an¬ 
gles. See Art. 27j for finish marks. 

Title. Lay out the guide lines for the title in the lower right 
hand corner of the sheet according to Fig. 45. Work up the 
following material into the same form as given: 


[ 41 ] 


























BACK REST 
FOR 

24 TURRET LATHE 

2 WANTED, 1 UPPER, 1 LOWER, UPPER DRAWN 
CAST STEEL—FINISHED 
SCALE FULL SIZE 

Use the method already given for balancing the title. It will 
insure good results and save time in the end. Art. 19a. 

Print the sheet number and the plate number in the upper 
half of the filing circle and the filing number in the lower half. 
Print the initials below the filing circle so that they are balanced 
on the verticle center line of the filing circle. 




Fig. 45 


PLATE 9 

TRACING OF PLATE 8 

Read the instructions for inking given in Art. 25e, lib. 


[ 42 ] 



























UNIVERSITY OF WISCONSIN 


DEPARTMENT OF DRAWING 
COURSE \ 


® A-'ll 


[ 43 ] 































PLATE 10 

SHOP DRAWING IN PENCIL. “BACK BONNET FOR VALVE” 


Given. The left side view, 1, and back view, 2, of a “Back 
Bonnet for Corliss Valve.” Fig. 46. 



Draw. The front and right side half section views. Scale- 
Half size. 

Use. The Back Bonnet is a cover plate, which closes the 
opening at the rear of the valve chamber of a Corliss engine. 


Conventions. View 1 of the Commutator Clamp Ring shown 
on sheet 207 is a half section. Read Art. 27k. 

The arc of a circle drawn through the centers of the holes in 
view 2, is a circular center line. Read Art. 27d. 

For methods of dimensioning small arcs read Art. 28j. 

Read Art. 28i on diametral dimensions on parallel lines. 

Title. Lay out the guide lines for the title in the lower right 
hand corner of the sheet according to the lay out given in Fig. 47. 

Letter the following material arranged as given: 

BACK BONNET FOR VALVE 
22 x42 CORLISS ENGINE 
4 WANTED—CAST-IRON FINISHED 
SCALE—HALF SIZE 



PLATE 11 

TRACING OF PLATE 10 

Read instructions for inking given in Art. 25e. 


[ 44 ] 











































FINISH ALU OVER 




UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE l 


[ 45 ] 















































PLATE 12 


SHOP DRAWING IN PENCIL. 

Given. The bottom view, 1, and back view, 2, of a “Stuff¬ 
ing Box Gland.” Fig. 48. 




Draw. The top and front quarter sections. Scale—Full size. 
Use. The gland is the piece which fits around the piston or 


“STUFFING BOX GLAND” 

valve rod, and when forced into the stuffing box, compresses the 
packing thus forcing the packing against the rod and making a 
steam tight joint as the rod moves into and out of the cylinder 
or steam chest. 

Analysis of Procedure. The original pencil layout for this 
sheet will look like that on sheet 208, that is all lines including 
the circular arcs are drawn longer than necessary and are as 
light as possible. The arcs are drawn first and the tangent lines 
drawn by placing a straight edge so that a line ruled along it 
will just touch the arcs. Art. 25c. 

Conventions. View lof the gland shown on sheet 209, illus¬ 
trates the quarter section. Read Art. 27k. 

Especial attention is called to the fact that there is an object 
line across the middle of the section view representing the edge 
of the lower half of the object, which is the result of the hori¬ 
zontal cut. 

Note the method of dimensioning the arc of f” radius on 
sheet. Art. 28j. 

Read Art. 281 for methods of dimensioning drilled holes. 

Title. Use the layout for the title on sheet 208 and the ma¬ 
terial given below. 

GLAND 

FOR 

THROTTLE VALVE STUFFING BOX 
1 WANTED—CAST-IRON- FINISHED 
SCALE-FULL SIZE 

Fill in the filing circle as usual. 


PLATE 13 

TRACING OF PLATE 12 

Read carefully Art. 251. It is essential that the arcs be drawn 
first, stopping them exaclty at the points of tangency to insure 
good joints. 


[ 46 ] 





























[47] 


































































© © 


1 ". 

z* 


■i 


7 “ 

77 . DRILL 
16 - 


FINISH ALL OVER 



UNIVERSITY OF WISCONSIN 

DEPARTMENT OF DRAWING 
COURSE I 


[ 48 ] 













































INCLINED PROJECTION 


Problem. Fig. 49. To draw the top, front and auxiliary 
views of a regular triangular prism. Bases perpendicular to 
the top plane and 75° to the front plane. One lateral face par¬ 
allel to the top plane. 


d 



Fig. 49 


1. Auxiliary view. 

2. Top view. 

3. Front view. 

1. Draw the top, front and auxiliary views of a regular hex¬ 
agonal prism. Bases perpendicular to the top plane and 30° to 
the front plane. Two opposite lateral faces parallel to the top 
plane. 

2. Draw the top, front and auxiliary views of a regular heg- 
agonal prism. Bases perpendicular to the top plane and 60° to 
the front plane. Two opposite lateral faces perpendicular to the 
top plane. 


3. Draw the top, front and auxiliary views of a regular square 
prism. Bases perpendicular to the top plane and 15° to the 
front plane. Lateral face 45° to the top plane. 

4. Draw the top, front and auxiliary views of a reguar square 



pyramid. Base perpendicular to the top plane and 30° to the 
front plane. Two opposite edges of the base parallel to the top 
plane. 

Problem. Fig. 50. To draw the top, front and auxiliary 
views of a right circular cylinder. Bases perpendicular to the 
front plane and 75° to the top plane. 


[ 49 ] 

















1. Auxiliary view. 

2. Top view. 

3. Front view. 


1. Draw the top, front and auxiliary views of a right circular 
cylinder. Bases perpendicular to the front plane and 30° to the 
top plane. 

2. Draw the top, front and auxiliary views of a right cone. 
Base perpendicular to the front plane and 60° to the top plane. 

Problem. Fig. 51. To draw the top, front and auxiliary views 
of a right cone. Base parallel to the top plane. Vertex above the 
base. Auxiliary view on a plane perpendicular to the front plane 
and 60° to the top plane. 

1. Top view. 

2. Front view. 

3. Auxiliary view. 

1. Draw the top, front and auxiliary view of a right cone. 
Base parallel to the front plane. Vertex in front of the base. 
Auxiliary view on a plane perpendicular to the top plane and 
45° to the front plane. 

2. Draw the top, front and auxiliary views of a right circu¬ 
lar cylinder. Bases parallel to the top plane. Auxiliary view 
on a plane perpendicular to the front plane and 30° to the top 
plane. 


[501 



Fig. 51 







PLATE 14 

SHOP DRAWING IN PENCIL. “BRACKET.” 


Given. The front view, 1, the end view, 2, section on AA, 3, 
and the true outline of the flanges, 4. Fig. 52. 

Draw. A shop solution, i. e. a solution in which the plotting 
of points is avoided by the use of auxiliary views. Scale—Full 
size. 

A solution should be indicated in a rough pencil sketch and 
submitted to the instructor for criticism before attempting to 
draw the plate. 

Use. The bracket is that part of a drill grinder which serves 
to support the V shaped holder into which the drill is placed for 
grinding. The cylindrical part whose axis is horizontal fits over 
and is clamped to a cylindrical projection from the frame of the 
machine. A cylindrical projection on the tool holder mentioned 
above fits into the inclined hole and is clamped just tight enough 
so that it may turn without jaring when the machine is in op¬ 
eration. 

Dimensioning’. The arrangement of dimensions on the 
sketch given is not the best, and in view of the fact that addi¬ 
tional or different views are necessary in the solution, the stu¬ 
dent will need to exercise his judgment in the disposition of 
dimensions so as to make the drawing read as clearly and easily 
as possible. 

As far as possible the dimensions for the section should be 
placed on the section rather than on the other views. 

The £•" hole in the web which joins the two cylindrical parts 
should be marked “core” as it is made by a core of sand in 
casting. 

The £" slots should be .cut with a V' milling cutter and note 
should be made to that effect in connection with the dimension. 


SECTION ON AA OUTLINE OP ♦LANGES 



The surface on which the heads of the studs will rest should 
be finished, and as it is only necessary to finish these spots, the 
operation should be noted by marking them “spot face.” 


[ 51 ] 























































In the solution of this problem it will be necessary to give 
some partial views, i. e. views which only show part of the ob¬ 
ject. In a case of this kind where it is necessary to consider 
part of the object broken away a ragged line is drawn, with the 
writing pen, across where the break occurs. 

When a section of some part of the object is shown in a sepa¬ 
rate view, a line should be drawn where the plane of the section 
cuts the object and labeled, as for instance AA, a note being 
made near the section view “section on AA.” 

All of the surfaces of this object are not to be finished and 
consequently the word “finished” must be omitted from the 
title. Those surfaces which are to be finished are marked in 


the view where they show as a line with an / as in Fig. 52, 
or the finish is indicated in some other way, such as by printing 
the word “bore,” “turn,” etc., with the dimension on a 
diameter. 

Title. Use the title layout given on sheet 208 and the material 
given below. 

DRILL REST BRACKET 
FOR 

YANKEE DRILL GRINDER 
1 WANTED—CAST-IRON 
SCALE-FULL SIZE 


PLATE 15 

TRACING OF PLATE 14 


[ 52 ] 


•MW 



[ 53 ], 





































































CHAPTER 5 


SECTIONS AND DEVELOPMENTS 


DEFINITIONS AND NOTATIONS 


33. A Profile plane is perpendicular to the horizontal and 
vertical planes of projection. The planes upon which the right 
and left side views are drawn are profile planes. 

Horizontal projections of points are indicted thus: a, b, c, 
etc. 

Vertical projections of points are indicated thus: a / , b', c\ 
etc. 

Profile projections of points, or projections of points upon 
auxiliary planes, are indicated thus: a", b", c", etc., or a' ", 
b' ", c' ", etc. 

Visible lines of an object are shown heavy and full. 

Hidden lines of an object are shown medium weight and 
dotted. 

Section planes and auxiliary planes are shown with a fine long 
dash and two short dashes. 

An element of a surface is any line of the surface. 

Elements cut by auxiliary planes are drawn fine and full. 

Planes are referred to by a capital letter, for example, plane 
T, plane S, etc. 

The trace of a plane is its intersection with one of the planes 
of projection. 

The horizontal trace is the intersection with the horizontal 
plane. The vertical trace is the intersection with the vertical 
plane, etc. 

A horizontal trace is indicated by the same small letter at 
each end of the trace, thus: a horizontal trace of the plane T is 
shown as tt, a vertical trace as t't', a profile trace as t"t", etc. 



[ 54 ] 











SECTIONS 

34. Section. When an object is cut by an imaginary plane, 
and the portion on either side of the cutting plane is removed, 
the surface exposed is called a section. 

Problem. To find the section of any object. 

General Method. Find the points in which the elements or 
edges of the object pierce the given section plane. 


e. m. a. 



DEVELOPMENT 

35. By the development of a surface is meant a plane area 
equal to that of the surface, and of such a form that it can be 
rolled up again into a surface. The development is formed by 
rolling the surface upon a plane until each element of the sur¬ 
face in turn comes into the plane. 

Problem. Fig. 53. To find the section of a regular 
prism. 

Method. Find the points in which the edges of the prism 
pierce the section plane. 

Problem. To find the section of an oblique prism. 

Method. Use the same method as for the regular prism. 

Problem. Fig. 55. To find the section of a right cir¬ 
cular cylinder. 


[ 55 ] 



Fig. 55 



Fig. 56 






































Method. Find the points in which the elements of the cylin¬ 
der pierce the section plane. 

Problem. To find the section of an oblique cylinder. 
Method. Same method as for the right circular cylinder. 
Problem. Fig. 57. To find the section of a regular 
pyramid. 



Method. Find the points in which the edges of the pyramid 
pierce the section plane. 

Problem. To find the section of an oblique pyramid. 

Method. Same method as for regular pyramid. 

Problem. Fig. 59. To find the section of a right cone. 
First Method. Find the points in which the circular ele¬ 
ments of the cone pierce the section plane. 


Second Method. Find the points in which the straight line 
elements of the cone pierce the section plane. 

Problem. To find the section of an oblique cone. 

Method. Use the second method. 

Problem. Fig. 61. To find the section of a sphere. 

Method. Find the points in which the circular elements of 
the sphere pierce the section plane. 

Problem. To find the section of any surface of revolu¬ 
tion. 

Method. Find the points in which the circular elements 
pierce the section plane. 



PROBLEMS 

36. In each of the following problems draw the projections 
of the given solid when cut by the given section plane. In each 
problem consider the part of the object on one side of the cutting 
plane removed. Section line the projections of the section. In 
the problems relating to cylinders and cones, find the points on 
the extreme elements in all views. 

In each problem find the true size of the section. 

In Figures 1 to 20 inclusive develop the lateral surfaces show¬ 
ing the section line in the development. 



















Fig. 59 



[ 57 ] 



Fig. 61 


























































FIG I 






/ 

S' 



F 16.2 


FIG.3 


FIG 4- 





FIG 6 




FIG 8 




FIG 15 



[ 58 ] 






































































PLATE 16 

SHOP DRAWING IN PENCIL,—“CHECK WASHER” 


Given. The front view, 1, and auxiliary view, 2. Fig. 62. 
Draw. The front, auxiliary and top views. Scale—Full size. 
Use. A washer of this kind is used in wooden roof trusses. 
Its function is to furnish a flat bearing for the head of a bolt 
which passes obliquely through a timber. The lugs on the 
under side are let into the wood to prevent it from slidiug. 

Title. Use the layout given for Plate 12. 

CHECK WASHER 
FOR 

WOODEN ROOF TRUSS 
24 WANTED—CAST-IRON 
SCALE-FULL SIZE 



PLATE 17 

TRACING OF PLATE 16 


[ 59 ] 
















[ 60 ] 


UNIVERSITY OF WISCONSIN 

department of drawing 

COURSE 2 


































CHAPTER 6 


INTERSECTIONS AND DEVELOPMENTS 


INTERSECTIONS 

37. Problem. To find Intersection of Any Two Solids. 
General Method. Find the points in which the edges or 
elements pierce the given surfaces. In order to find the required 



piercing points in some problems it is necessary to pass auxiliary 
planes through the edges or elements and cutting simple sections 
from both solids. The intersections of these sections will de¬ 
termine points on the required line of intersection. 



PROBLEMS 

38. In each of the problems on page 64 draw three views of 
the intersecting solids. In each problelem consider the elements 


[ 61 ] 





















































or edges of one of the solids ended where they strike the surface 
of the other. 

Develop the lateral surfaces of the solids, showing the inter¬ 
section line in the development. 



O 




r 



[ 62 ] 




Fig. 66 






































z \ 

\/ 1 





\ * 

or 





/ 




Fig. 67 


f 



® J 

/ttT- 

/A 

[ irs 

i 

Us' / 

i . / 

T/ 

s \ 

\t n 

\\ 

V/ 

i/ 

t\ m h 

/ >1 Jr" 

^//\ 

j \ 

4" ^ \ 


-" \ 




Fig. 68 


* 

[ 63 ] 
















































[ 64 ] 


-+ 



























































PLATE 18 

SHOP DRAWING IN PENCIL “DRAFT CHEST” 


Given. Incomplete top, 1, and front, 2, views and end view, 
3, of a draft chest for a hydraulic turbine. Fig. 69. 

Draw. Complete top, front and end views. Scale—to 
1 '— 0 ". 




An rivets jit c/'crme^ev* 



Use. The part here shown is only the lower half of what is 
known as the draft chest. The upper half is simply a semi- 
cylindrical plate. The turbine wheels are placed one at each 
end of this cylindrical shell and with their axes parallel to the 


axes of the shell. Water passes through the wheels into the 
cylindrical part and thence down the conical outlet. 

Allowance for thickness of metal. When working with 
plate metal the thickness of which is considerable, it is neces¬ 
sary in making the patterns or developments to make allowance 
for the effect of the thickness on the size of the plate after it is 
bent to shape. If a pattern be made from the inside meas¬ 



urements of a cylinder, the cylinder will be too small when 
bent into shape, due to the compression of the layers of metal 
near to the inside of the cylinder. While the inside layers are 
compressed the outer ones are stretched. It is found that in 
flat plates a surface through the middle of the plate does not 
suffer change of dimensions in bending, and hence it is custom¬ 
ary to lay oat the pattern for this neutral surface. For instance, 
if a cylinder of 3 ft. inside diameter is to be made from material 
i in. thick the pattern would be drawn for a cylinder 3 ft. 2 in. 
diameter. 


[ 65 ] 





















































The original layout of the student’s drawing should represent 
this neutral surface, and from it he should make the following 
plate of developments before going further, The first drawing 
should be finished afterward. 

Intersection Curves. Notice that the metal forming the 
conical outlet is flanged to fit the cylinder. Hence the inteasec- 
tion curve plotted will not be an actual intersection line between 
the cone and cylinder, but a line where the neutral surface of 
the flange joins that of the cone. 


Title. Use the following material and the layout given in 
Fig. 70. 

DETAIL OF BOILER WORK 
FOR 

NO. 1 DRAFT CHEST 
49 HYDRAULIC TURBINE 
l" TO 1-0 


PLATE 19 


TRACING OF PLATE 18 























































PLATE 20 


SHOP DRAWING IN PENCIL FROM PLATE 18—DEVELOPMENT 


Given. The layout of Plate 20, including the intersection 
line. Scale to 1/— 0". 

Draw. The development of the conical and cylindrical sur¬ 
faces. Scale to 1'—0". 

Development. The conical outlet is divided into three parts, 
two of which are alike except that they are for opposite sides 
and the same pattern may be used for both by simply bending 
the metal in opposite directions. This is also true for the semi- 
cylindrical parts. 

The usual rule is to make the distance from the center line of 


rivets to the edge of the metal just one and one-half times the 
diameter of the rivets. This distance is one-half the lap for a 
single riveted lap joint. 

The width of the flange, which in this case will be equal to 
the lap, must be allowed outside of the intersection. It should 
be laid out by#striking arcs of radius equal to the width of the 
flange with their centers on the development of the intersection 
line and drawing a curve tangent to these arcs. 

Title. Same as for Plate 20. 


PLATE 21 

TRACING OF PLATE 20 


[ 68 ] 


CHAPTER 7 


ISOMETRIC AND CABINET PROJECTION 


39. Isometic Projection is a method of representing an 
object in one view. This view shows more than one face of an 
object thus giving the effect of a picture. Because the theory 
involved is much simpler and its application is much easier this 
method is often preferable to the exact pictorial representation 
afforded by perspective. An isometric drawing of an ob- 




Fig. 71 


Tha projections of the three nearest edges of the cube a b, be 
and b d make equal angles with each other (120°). 

Under the conditions stated the edges of the cube all make 
the same angle with the plane of projection. Their projections 
are, therefore, all foreshortened in the same ratio. This fore¬ 
shortening is generally disregarded, and the lines made actual 
lengths in the drawing. The only effect of this is to change the 
scale of the drawing. 



ject is usually termed the “isometric” of the object. Isometric 
is used for illustrating parts of machines or structures where the 
orthographic is hard to read, or for those who are unaccustomed 
to reading working drawings. It is also used in patent office 
drawing. 

40. Derivation of Axes. If a cube be placed so that one 
of its diagonals is perpendicular to a plane of projection, the 
projection of the cube upon the plane wilt appear as in Fig 71 A. 


It has been stated that the cube was placed with a diagonal 
perpendicular to the plane of projection. Its position is further 
limited by turning it about this diagonal until the projections of 
two of the near edges make 30° with a horizontal line, while the 
third is vertical. Fig. 71B. These three lines represnt the di¬ 
mensions of the cube, and consequently its isometric may be 
drawn by laying off lengths parallel to these lines. They are 
called the isometric axes. 


[ 69 ] 















The following is a summary of the underlying principles of 
isometric drawing: 

(a) The axes represent three lines mutually at right angles , 
thus corresponding to length , breadth and height. All measure¬ 
ments on the drawing must be laid off parallel to these axes. 




(&) Parallel lines in the object are parallel in the drawing. 
Vertical lines are drawn vertical. 

41. Non-isometric Lines. Lines of the object which cannot 



Fig. 74 


be drawn parallel to one of the three axes are termed non-iso¬ 
metric lines. Such lines must be drawn by co-ordinates taken 
parallel to the axes as shown in Fig. 72. 


(a) The work of laying out non-rectangular plane figures 
may be simplified if they can be inscribed in rectangles. Fig. 73. 



(■ b) Three dimension figures maybe laid out in a manner simi¬ 
lar to that shown for plane figures by introducing a third co¬ 
ordinate. Fig. 74. 




(c) Non-rectangular solids which can be inscribed in a rectan¬ 
gular prism may be drawn as in Fig. 75. 

42. Approximate Isometric Circles. Circles may be 
drawn more easily, though not so accurately, by the following 
method. Draw first the isometric of the square inscribing the 


[ 70 ] 









































circle. The center d, Fig, 76, for the short radius r is found 
by striking an arc with center at a and radius ae = i ab, r=de. 
The center of the long radius R is located by striking an arc 
with its center at e with radius = ab, R =ec = ab. 

43. Cabinet Projection. The uses and fundamental prin¬ 
ciples are very similar to Isometric Projection. Fig. 77. Here 
one face of the object is parallel to the plane of projection. 
There are three axes, one horizontal, one vertical and one at 45°. 
Actual lengths are laid off parallel to the horizontal and vertical 
axes. One-half actual lengths are laid off parallel to the 45° 
axis- Circles in planes parallel to the plane of projection show 
as true circles. All others must be plotted. 




Fig. 77 


PLATE 22 


Make an isometric and a cabinet drawing of the pyramid de¬ 
scribed in the following problem. Place the top and front views 
in the middle of the sheet in orthographic projection. To the 
right of this draw the cabinet and to the left the isometric. Ink 
in the drawing on the paper. 

Title. Beneath each view print the name corresponding. 
Isometric, Orthographic and Cabinet in vertical capitals i/' 
high. 


Draw. A hexagonal pyramid 3j" high; side of hexagona 
base It" long. Half way up the sides of the pyramid is a groove 
extending entirely around the pyramid. This groove is formed 
by removing the portion of the pyramid between two cuts, each 
t" deep (measured parallel to the plane of the cut and perpen¬ 
dicular to the edge of the hexagon). The planes of both cuts 
are parallel to the planes of the base of the pyramid. The per¬ 
pendicular distance between the planes of the two cuts is l ". 
(From Tracy’s Mechanical Drawing.) 


[ 71 ] 







PLATE 23 


Make a working drawing of a wooden box. Scale- Half size. 



The top of the box is 10" x 16" OA (over all), bottom 8|- x 12i" 
OA; depth 3" OA. Opposite sides have the same slope. The 


bottom board laps over the sides and the sides lap over the ends. 
Thickness of material . A vertical partition which is parallel 
to the longer edges divides the box into two equal compartments. 
The upper part of this partition is cut into the form of a handle 
as shown in Fig. 78. Show all dimensions. Ink on paper. 

A note should be printed on the drawing in inclined lower 
case letters as follows, — Hard wood—all joints glued and nailed 
—thickness of material 
Title. 


TOOL TRAY 
SCALE—HALF SIZE 


PLATE 24 

Make an isometric of the box in Plate 23. Copy the note and 
title. Show all dimensions. Ink on paper. 


[ 72 ] 










One copy del. to Cat. Div. 

|UN 28 *911 


i 


ft 





/ 







4 



library of congress 


